# Test 1c: Oster (2019) δ Bounds

*δ measures proportional selection on unobservables vs observables needed to drive β to zero.*

*If δ_pre < δ_post, unobservables matter more pre-opening (confounders hypothesis).*

*|δ| > 1 means unobservables would need to be MORE important than observables to explain away the result — robust.*

| Period | β (uncontrolled) | β (controlled) | R² (unc) | R² (ctrl) | R²_max | δ | N |
|:---|---:|---:|---:|---:|---:|---:|---:|
| Pre-opening | 47.440 | 21.750 | 0.095 | 0.147 | 0.191 | 0.721 | 73 |
| Post-opening | 7.835 | 68.222 | 0.029 | -0.080 | -0.104 | -0.249 | 288 |

**δ_pre = 0.721, δ_post = -0.249**
*|δ_pre| ≥ |δ_post| → pre-opening result NOT more vulnerable to unobservables → against confounders hypothesis.*

*R²_max = min(1.3 × R²_ctrl, 1.0) following Oster (2019).*
*Uncontrolled: ca_gdp ~ Z. Controlled: ca_gdp ~ Z + all controls + structural.*
*Transition economy openers only.*